Synchronization of coupled neural networks with infinite-time distributed delays via quantized intermittent pinning control

Abstract

How to deal with the effect of infinite-time delay and maximize rest width is the main difficulty for intermittent control techniques. This paper considers asymptotic synchronization of coupled neural networks (CNNs) with bounded time-varying discrete delay and infinite-time distributed delay (mixed delays). A quantized intermittent pinning control scheme is designed to save both channel resources and control cost and reduce both the amount of transmitted information and channel blocking. Two weighted integral inequalities are first established to deal with the infinite-time distributed delay. Based on weighted double-integral inequalities, novel Lyapunov–Krasovskii functionals with negative terms are designed, which can reduce the conservativeness of the results. Some sufficient conditions in the form of linear matrix inequalities are obtained to ensure that the CNNs asymptotically synchronize to an isolated system. Moreover, the relationships between the control width, rest width, and convergence rate are explicitly given. Furthermore, an optimal algorithm is provided to increase the rest width as large as possible. As special cases, the synchronization of the CNNs with quantized pinning control and quantized intermittent control are also considered, respectively. Finally, numerical simulations are provided to illustrate the effectiveness of the theoretical analysis.